Integer--valued functions, Hurwitz functions and related topics: a survey

Hurwitz 类数的加权递归

Weighted Recursions for Hurwitz Class Numbers

本文通过向量值全纯投影算子作用于 mock 模形式，建立了 Hurwitz 类数的加权新递归，将偶判别式与奇判别式的类数解耦，并利用表示论将向量值模形式空间与经典新形式和老形式空间关联，借助标量情形中不可用的向量值尖点形式空间的消失性。

On adelic Hurwitz zeta measures

In this paper we construct a $\hat\mathbb{Z}$-valued measure on $\hat\mathbb{Z}$ which interpolates $p$-adic Hurwitz zeta functions for all $p$.

Overpartition $M2$-rank differences, class number relations, and vector-valued mock Eisenstein series

We prove that the generating function of overpartition $M2$-rank differences is, up to coefficient signs, a component of the vector-valued mock Eisenstein series attached to a certain quadratic form. We use this to compute analogs of the class number relations for $M2$-rank differences. As applications we split the Kronecker-Hurwitz relation into its "even" and "odd" parts and calculate sums over Hurwitz class numbers of the form $\sum_{r \in \mathbb{Z}} H(n - 2r^2)$.

On the sum relation of multiple Hurwitz zeta functions

In this paper we shall define a special-valued multiple Hurwitz zeta functions, namely the multiple $t$-values $t(\boldsymbolα)$ and define similarly the multiple star $t$-values as $t^{\star}(\boldsymbolα)$. Then we consider the sum of all such multiple (star) $t$-values of fixed depth and weight with even argument and prove that such a sum can be evaluated when the evaluations of $t(\{2m\}^n)$ and $t^{\star}(\{2m\}^n)$ are clear. We give the evaluations of them in terms of the classical Euler numbers through their generating functions.

C-多项式与LC-函数：迈向Hurwitz zeta函数的推广

C-polynomials and LC-functions: towards a generalization of the Hurwitz zeta function

本研究定义了与解析函数f相关的C-多项式、P-多项式及推广s^z的复变函数，进而构造出推广Hurwitz zeta函数的LC-函数，分析了三者性质与关联，开辟了具类Riemann zeta函数方程的LC-函数新研究方向。

确定不定性：关于连接黎曼、Hurwitz和狄利克雷ζ、η和β函数的积分的评估

Determining the Indeterminate: On the Evaluation of Integrals that connect Riemann's, Hurwitz' and Dirichlet's Zeta, Eta and Beta functions

本文研究了连接黎曼、Hurwitz和狄利克雷ζ、η和β函数的积分的评估，揭示了与本质奇点相关的不定性，并提出了新的符号和方法来处理这些积分。